I really like both names. I do think you will run into a lot of people who say Care-a though so if that's something that will annoy you or get old I would pick Claire.
I voted Claire but was also coming to suggest Clara (Claire was always my #1 girl's name but my cousin beat me too it). Cara will get mispronounced a lot if you live in the states, so you may wind up correcting a lot of people with that one.
Another vote for Claire and I actually really like Clara too. I would not have pronounced that as Car-a myself so I also would suggest being prepared to always be correcting people.
Re: Claire or Cara